Among the seven types of crystal systems orthorhomic crystal system posses both primitive as well as non-primitive unit cells i.e. face centred body centred rnd centred and simple cubic but the cubic system posses primitive , body centred and face centred arrangements only.

My question is if face centred is possible in cubic system why is not end centred type of unit cell arrangement possible in cubic system if there is no sort of hindrance in vacant space as in orthorhombic which posses all types of unit cell arrangements.

$\begingroup$I'm a bit confused. What's going on here? Essence of the cubic system is equivalence of a, b and c axes, namely, presence of 3-fold axis in the body-diagonal direction of the cube. There's no chance of "base-" centred cubic.$\endgroup$
– user6983Jun 29 '14 at 13:06

1 Answer
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First, a note: the classification of crystal systems, or the reduction of possible lattice types into primitive Bravais lattices, has nothing to do with “space available” or “hindrance”. It is purely a mathematical property having to do with the symmetry of the lattices.

$\begingroup$i got what you had to say about the space thing but i am still confused as. to why cubic systems do not possess end centred arrangement if face centred is possible?$\endgroup$
– user1811Jul 16 '13 at 15:03

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$\begingroup$@AanalDesai it is possible to have a base centered cubic system, but it is not a minimal representation of the system. Just like the unit cell must be the smallest cell that can reproduce the full periodic system by a set of translation, the Bravais lattices are by definition the smallest lattices. Imagine a base-centered cubic system (drawing on the left): you can represent this particular lattice as “base-centered cubic”, but you can also view it as a “simple tetragonal” lattice… and the second representation features a smaller unit cell, hence it is the irreducible one.$\endgroup$
– F'xJul 16 '13 at 19:03

$\begingroup$I had one more query, Wouldn't a face centred simple cubic be an in-centred tetragonal then..?$\endgroup$
– user1811Sep 16 '13 at 4:46